Problem Statement

You have decided to give an allowance to your child depending on the outcome of the game that he will play now.

The game is played as follows:

• There are three "integer panels", each with a digit between 1 and 9 (inclusive) printed on it, and one "operator panel" with a + printed on it.
• The player should construct a formula of the form X + Y, by arranging the four panels from left to right. (The operator panel should not be placed at either end of the formula.)
• Then, the amount of the allowance will be equal to the resulting value of the formula.

Given the values A, B and C printed on the integer panels used in the game, find the maximum possible amount of the allowance.

Constraints

• All values in input are integers.
• 1 \leq A, B, C \leq 9

Sample Input 1

1 5 2

Sample Output 1

53

The amount of the allowance will be 53 when the panels are arranged as 52+1, and this is the maximum possible amount.

Sample Input 2

9 9 9

Sample Output 2

108

Sample Input 3

6 6 7

Sample Output 3

82

Problem Statement

Our world is one-dimensional, and ruled by two empires called Empire A and Empire B.

The capital of Empire A is located at coordinate X, and that of Empire B is located at coordinate Y.

One day, Empire A becomes inclined to put the cities at coordinates x_1, x_2, ..., x_N under its control, and Empire B becomes inclined to put the cities at coordinates y_1, y_2, ..., y_M under its control.

If there exists an integer Z that satisfies all of the following three conditions, they will come to an agreement, but otherwise war will break out.

• X < Z \leq Y
• x_1, x_2, ..., x_N < Z
• y_1, y_2, ..., y_M \geq Z

Determine if war will break out.

Constraints

• All values in input are integers.
• 1 \leq N, M \leq 100
• -100 \leq X < Y \leq 100
• -100 \leq x_i, y_i \leq 100
• x_1, x_2, ..., x_N \neq X
• x_i are all different.
• y_1, y_2, ..., y_M \neq Y
• y_i are all different.

Sample Input 1

3 2 10 20
8 15 13
16 22

Sample Output 1

No War

The choice Z = 16 satisfies all of the three conditions as follows, thus they will come to an agreement.

• X = 10 < 16 \leq 20 = Y
• 8, 15, 13 < 16
• 16, 22 \geq 16

Sample Input 2

4 2 -48 -1
-20 -35 -91 -23
-22 66

Sample Output 2

War

Sample Input 3

5 3 6 8
-10 3 1 5 -100
100 6 14

Sample Output 3

War

Problem Statement

You are given strings S and T consisting of lowercase English letters.

You can perform the following operation on S any number of times:

Operation: Choose two distinct lowercase English letters c_1 and c_2, then replace every occurrence of c_1 with c_2, and every occurrence of c_2 with c_1.

Determine if S and T can be made equal by performing the operation zero or more times.

Constraints

• 1 \leq |S| \leq 2 \times 10^5
• |S| = |T|
• S and T consists of lowercase English letters.

Sample Input 1

azzel
apple

Sample Output 1

Yes

azzel can be changed to apple, as follows:

• Choose e as c_1 and l as c_2. azzel becomes azzle.
• Choose z as c_1 and p as c_2. azzle becomes apple.

Sample Input 2

chokudai
redcoder

Sample Output 2

No

No sequences of operation can change chokudai to redcoder.

Sample Input 3

abcdefghijklmnopqrstuvwxyz
ibyhqfrekavclxjstdwgpzmonu

Sample Output 3

Yes

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

• All values in input are integers.
• 1 \leq N \leq 10^5
• 1 \leq M \leq 10^9

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001